Join the Mathematics and Statistics Department for a variety of stimulating math talks. We will meet every Monday from 3:10 to 4 p.m. (unless otherwise noted). For those who are on our distribution list, instructions on how to join each virtual meeting will be sent to your Kenyon email. If you would like to be added to the distribution list, please email Emily Teater at teater1@kenyon.edu.

Spring 2024

Smallwood Family Professor of Mathematics at Harvey Mudd College Arthur T. Benjamin will be visiting campus to share his work with undergraduate students and combinatorial proofs.

"Some of my favorite combinatorial proofs have been discovered with undergraduates. We'll present clever counting arguments and beautiful bijections involving binomial coefficients, squares, cubes, and Fibonacci numbers. Sum-thing fun for everyone!"

Join us on Wednesday, Jan. 30, at 3:10 p.m. in Tomsich 101 to hear this exciting presentation about counting and combinatorial proofs. We hope to see you there!

Smallwood Family Professor of Mathematics at Harvey Mudd College Arthur Benjamin will be visiting campus to share his well-known "Mathemagics!" presentation with Kenyon. Come see the wonders of magic and math combined!

In his entertaining and fast-paced performance, mathematician and magician Benjamin will demonstrate and explain how to mentally add and multiply numbers faster than a calculator, how to memorize 100 digits of pi, how to figure out the day of the week and of any date in history and other amazing feats of mind. He has given three TED Talks, which have been viewed over 50 million times. Reader's Digest calls him America's Best Math Whiz.

Join us on Wednesday, Jan. 24, at 7 p.m. in the Higley Auditorium to hear this exciting presentation from Benjamin. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we present a double feature from two of our seniors.

Phillip Diamond will be sharing his research titled "An Average Strategy for Nonlocal Games." Nonlocal games, played between two players and a referee, demonstrate the physical significance of quantum entanglement. If the players share an entangled quantum state, they can win a nonlocal game more often than is classically possible. The standard method for calculating the players' winning percentages uses a tensor product, an operation difficult to visualize. Over summer 2023 Phillip's group studied a new perspective on the math underlying the computation of winning percentages, one involving taking component-wise averages on a grid. With this new perspective, they reproduced optimal winning strategies for the simplest nonlocal game, the 'CHSH' game, and also had some success working with more complicated games.

Casey Flueckiger will also share her research titled "Comparative Regression Modeling of Inequality at DAACS Documented Sites of Enslavement." This summer research project focused on developing regression models to better understand inequality within and between sites of enslavement in the United States and the Caribbean through ceramic sherds from archaeological sites. Initial research focused on comparing contexts within sites. Other models were used to compare different sites and regions over time. No statistically significant differences were found between contexts at specific plantations. However, the lack of statically significant differences does not indicate a lack of inequality between enslaved and free populations. Bootstrapping and nonparametric smoothing were used to investigate patterns of ceramic ware possession over time. These models help us understand cultural trends and ceramic popularity for individuals historically and regionally.

Join us on Monday, Jan. 29, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we present a double feature from two of our juniors.

Leif Schaumann will be sharing his research titled "Fractals From Thue-Morse Turtle Curves." Turtle graphics are a useful way to visualize a sequence. We start with a “turtle” sitting in the plane at (0, 0), facing east. We then provide the turtle a series of instructions such as “move forward 2 units” or “turn left 60 degrees.”  For any sequence using some finite set of symbols, we can convert that sequence into a sequence of instructions for the turtle by choosing a function that maps symbols to instructions. The turtle adjusts its position and heading accordingly as it reads the instructions, and as it moves, it traces a line behind it. We call this line the “turtle curve.” In a 2005 paper, Professor Holdener and Jun Ma revealed that when this method is used to visualize the well known Thue-Morse sequence, with certain parameters, the resulting turtle curve approximates the Koch snowflake, a classic fractal object. Our work from last summer explores this connection with a new approach, obtaining a characterization of the parameters which cause these Thue-Morse turtle curves to approximate the Koch snowflake. In the process, we obtained more general results which predict when other interesting fractal curves can be produced.

Braeden Singleton will also share his work with Maria Angelica Cueto of the Ohio State University titled "Creating Programs to Compute Tropical Interpolating Curves." Tropical geometry is a type of projective geometry in which the operations of addition and multiplication are redefined. Exploring what polynomials look like and the problem of interpolation, we introduce a user-friendly graphical user interface (GUI) for Python. The program is built with Tkinter and SageMath to display plane tropical curves and their associated Newton subdivision. This included three programs allowing for the display and investigation of tropical curves.

Join us on Monday, Feb. 5, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Declare your love for math! Celebrate with snacks and treats during this special Math Monday event. We will also be doing some fun, themed math activities for the occasion. Take this opportunity to declare your MATH major or MATH or STAT minor during the celebration!

Join us on Monday, Feb. 12, at 3:10 p.m. in Hayes 109 for this exciting celebration of mathematics. We hope to see you there!

Biological processes usually happen across multiple scales. While it is easy for us to focus on the scales visible to our naked eyes, the processes at micron scales play a significant role in nature and can be quite counter-intuitive. In this presentation, Hanliang Guo will talk about the mathematical modeling of biological flows at the micron scale. Specifically, he will first present a toy model in which two hydrodynamically-coupled cylinders "dance" in various modes inside confinement, and then show how simple mathematical modeling of a biological system can potentially provide fundamental insights into the early evolution of multicellular organization.

Join us on Monday, Feb. 19, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Hanliang Guo, assistant professor of mathematics and computer science at Ohio Wesleyan University. We hope to see you there!

In this talk, we will give an introduction to homomorphic encryption, often hailed as the "holy grail" of cryptography. This groundbreaking technology stands at the forefront of privacy preservation, offering a glimpse into the future of secure data processing. Our exploration begins with a comprehensive overview of its evolution, tracing back to its historical roots and the groundbreaking mathematical principles that underpin it. We will mention some real-world applications and use cases, illustrating the transformative potential of homomorphic encryption across various industries. We will also give a demonstration of how homomorphic encryption works through a simple yet enlightening example: executing a secure query within a semi-honest encrypted key-value database.

Bahattin Yildiz earned his Doctor of Philosophy degree from the California Institute of Technology in 2006. Over the span of his 15-year academic tenure, he has held professorial positions at several institutions. His most recent academic role was a dual appointment in the Department of Mathematics and the School of Informatics, Computing, and Cyber Systems at Northern Arizona University. Following his academic career, Yildiz transitioned to the industry, where he served as a senior research scientist at Intel Labs for approximately one and a half years. Subsequently, he was appointed director of security research at LG Electronics. In his current role, he oversees the Advanced Security Team, focusing on research and development in post-quantum cryptography and homomorphic encryption. His primary research interests include post-quantum cryptography, privacy preserving technologies and coding theory. Yildiz has supervised four doctoral and ten master's students. Additionally, he has authored and co-authored approximately 75 scholarly articles in the fields of coding theory, combinatorics and cryptography.

Join us on Monday, Feb. 26, at 3:10 p.m. in Hayes 109 to hear this exciting virtual presentation from Bahattin Yildiz. We hope to see you there!

In this talk, Rachel Diethorn, assistant professor of mathematics at Oberlin College, will tell you a little bit about her research in commutative algebra with a focus on her favorite object: a free resolution. Free resolutions are central objects in commutative algebra that store important data describing commutative rings. In some sense, free resolutions approximate commutative rings by simpler algebraic objects and can reduce complicated algebraic problems to ones that can be handled using basic tools from linear algebra.

Join us on Monday, Mar. 25, at 3:10 p.m. in Hayes 109 to hear this exciting virtual presentation from Rachel Diethorn. We hope to see you there!

Fall 2023

Our first Math Monday of the new year is set for August 28. Please join us for a Math Nature Walk, which will start at 3:10 p.m. Plan to meet at the outside doors to Hayes Hall. We will leave shortly after 3:10.

A drink station will be available before the walk, but you are encouraged to bring your own water bottles. This is your chance to catch up with old friends and meet new ones as we say hello to all our fellow math and stats faculty and students. We hope to see you there!

Meet and greet with your fellow math/stat students and the math and statistics faculty at this year's First-Year Welcome Tea. Say hello to our math community and hear about all the exciting news in mant and statistics. Learn about exciting opportunities and our Math Monday series.

Join us on the Peirce Patio (weather permitting) at 3:10 p.m. on Monday, Sept. 4. We will be offering a variety of snacks with lemonade and iced tea. Celebrate another year of mathematics and statistics here at Kenyon. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we present a double feature from two of our juniors.

Kyle Kelley spent the summer researching addsub graphs. Addsub configuration graphs depict the relationship between ordered pairs of integers modulo n and a specified "move." We consider the structures of addsub graphs, their symmetries, and their relation to subgroup structures. We also investigate the number of weakly connected components in addsub graphs and their relation to the structure of the integers modulo n. Finally, we discuss possible generalizations of configuration graphs to other groups and to higher dimensions.

Sammy Shrestha worked extensively on research involving virtual reality. Virtual reality (VR), a branch of extended reality (XR), is the computer-generated simulation of a three-dimensional environment, which allows for immersive user interaction. Understanding user interactions and behavior within VR is necessary for creating meaningful and realistic VR experiences. This involves analyzing and interpreting behavioral data collected from VR experiences, which can provide valuable and unique insights for continuous improvement and practical design of immersive virtual environments.

Join us on Monday, Sept. 11, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we present a double feature from one of our juniors and one of our seniors.

Vaughn Hajra worked this summer with research involving modeling recovery and fatigue in athletics. What factors are highly correlated with injury and fatigue? How can we apply statistical models in a practical way to benefit athletes? With an emphasis on bayesian hierarchical modeling, we can answer some of those questions.

Khue Tran spent the summer working on her research titled "Comparing Nonparametric Tests for Interaction in Two-way ANOVA with Balanced Replications." When the data are normally distributed, the F-test is the most powerful and recommended procedure for detecting interaction in two-way ANOVA. Previous research has shown that nonparametric test procedures are more powerful when the data are not normally distributed. We computed extensive null critical values for the aligned rank-based tests (APCSSA/APCSSM) in additional settings where the numbers of levels of the factors are between 2 and 6. The performance of these new procedures, the ANOVA F-test for interaction, the adjusted rank transform test (ART), Conover’s rank transform procedure, and the raov function in the Rfit package were compared using Monte Carlo simulations. There is no single dominant test that detects interaction effects for non-normal data, but nonparametric procedures APCSSM and ART are definitely more powerful than the F-test for Cauchy data. Our hope is that these recently developed nonparametric methods will be more widely considered.

Join us on Monday, Sept. 18, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Professor of Mathematics Noah Aydin was on sabbatical last year and spent six months in Algeria as a Fulbright scholar. In this informal presentation, he will talk about his experiences and his adventures there as well as some of his other activities during the past year. He will share some stories and many pictures from Algeria and Morocco.

Join us on Monday, Sept. 25, at 3:10 p.m. in Hayes 109 to hear this exciting presentation about Aydin's sabbatical. We hope to see you there!

Are you interested in a summer or mid-semester internship? Are you curious about what internships look like in math or related fields? Join us for a Student Internship Panel. Come hear your peers discuss their recent internships and share their experiences with you. Lori Gastin from Kenyon’s Career Development Office (CDO) will also share some details about how the CDO can support you in the process of securing an internship.

This year's panel includes students from our junior and senior years who have worked for a variety of businesses and institutions:

Viet Dang '24 - Data Management Consulting Intern at Infoverity

Kyle Kelley '25 - Moravian University's REU: Research Challenges of Computational Methods in Discrete Mathematics

Kate Lengel '24 - Platform Solutions Summer Analyst at Goldman Sachs

Connor Moss '25 - Data Science/AI Intern at Langar Holdings

Harshal Rukhaiyar '24 - Business Consulting at TietoEvry

Sammy Shrestha '25 - Research Intern in Statistics at the Ohio State University

Join us on Monday, October 2, at 3:10 p.m. in Hayes 109 to hear this exciting presentation about this year's student interns and how you too can get involved. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we present a full panel from some of our juniors and sophomores.

Jimmy Baker's research was to classify protein function by the geometric structure and chemical composition of the protein-ligand binding site using various mathematical and statistical methods. They classified the proteins according to a method we called CDPA.

Cael Elmore will discuss the research conducted at the University of Iowa on modeling healthcare worker behavior within hospital environments. Leveraging an extensive dataset comprising over 44 million observations from diverse healthcare facilities, they developed sophisticated models of healthcare worker interactions with patients and each other. Cael will share insights into the application of these models in driving simulations aimed at enhancing our understanding of hospital-acquired infection prevention.

Drake Lewis will share research done on optimizing pose graphs using the minimum cycle basis. In researching graph theory, the goal was to create code in Python and optimize a pose graph using the minimum cycle basis (MCB) and all pairs shortest path (APSP). Starting with all pairs shortest path, it was constructed using the lexicographical Dijkstra algorithm, ensuring a consistent APSP. Using only positive weighted graphs (a parameter of Dijkstra's algorithm), the true shortest paths for any undirected graph were found. With an accurate APSP checked with results from Networkx, the MCB was constructed by use of the Horton set and Gaussian Elimination. In doing so,  MCB for any given graph (the biggest one tested had 808 nodes and 827 edges) was computed, with its results also checked by Networkx. Now, while there wasn't enough time to learn the techniques necessary to implement code to optimize a pose graph using the MCB, we learned about its process and its influence in robotics because of its ability to minimize the error between predicted and observed data.

Join us on Monday, Oct. 16, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

While Pascal's triangle is often taught within the context of elementary statistics, it holds great significance in subjects like combinatorics. In algebraic computation, Pascal's Triangle can be utilized to expand powers of binomials, but how exactly can an application like this generalize? We explore how triangles that generalize Pascal's hold secrets to efficiently computing everything from the betti numbers for projective hypersurfaces, to bounding the number points at which the partial derivatives of homogeneous polynomials can vanish in projective space.

Join us on Monday, Oct. 23, at 3:10 p.m. in Hayes 109 to hear this exciting presentation about Benjamin Castor's research. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we have Irina Beshentseva '24 and Michelle Polak '25 who worked with Professor of Mathematics and Computer Science James Skon this summer.

This project delves into the design and implementation of an open-source, cloud-managed Wi-Fi platform, featuring numerous functionalities typically exclusive to commercial managed enterprise Wi-Fi platforms. These capabilities encompass the centralized management of multiple Access Points (APs), the configuration of multiple zones and Service Set Identifiers (SSIDs), the establishment of per-user Virtual Local Area Networks (VLANs), and the implementation of user monitoring and control. The goal of this project is to develop a Wi-Fi system that extends enterprise-level networking features to households and low-income organizations, all at minimal to no cost. This section of the project focuses on the development of a web portal application and an API designed to interact with Skon's Raspberry Pi Wi-Fi software. This cloud-based web portal enables users to remotely manage various aspects of their network: access point and radio configurations, SSIDs, zones, individual network user-passphrase pairs, and per-user network data. The web portal is built using the Ruby on Rails framework and hosted on Amazon Web Services.

Join us on Monday, Oct. 30, at 3:10 p.m. in Hayes 109 to hear this exciting presentation and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Given a metric space, an isometry is a transformation which preserves the distance. I will be interested in isometries from a normed space X to another normed space Y. Translation, reflection and rotation are some well-known examples of isometries. 

On the other hand, we are familiar with projections. An operator P from a normed space X to X is a projection if P2 = P. Projections are building blocks of many otheroperators and are easy to understand.

This talk will explore the connections between the two operators described above. I will give plenty of examples of both types of operators on finite and infinite dimensional spaces.

Join us on Monday, Nov. 6, at 3:10 p.m. in Hayes 109 to hear this exciting presentation by Dey. We hope to see you there!